1. Field of the Invention
The invention concerns a method of calculating weighting coefficients used in an analytical digitizer for signal processing. A known technique in the field of telecommunications and sensing is to process a real signal after digitizing it analytically, i.e. after representing it by a sequence of complex samples. The complex samples can be represented in Cartesian co-ordinates (x, y) or in polar co-ordinates (r, .theta.), the temporal increment of which depends only on the bandwidth of the signal represented. The Cartesian form of representation is more advantageous for frequency filtering whereas the polar form is more advantageous for frequency conversion and phase or frequency estimation.
2. Description of the Prior Art
A prior art analytical digitizer implemented in analog components has two channels each including a modulator, a filter, an amplifier and a sampler. An oscillator supplies two sinusoidal signals in phase quadrature to respective modulators which also receive the signal to be processed. The frequency of this oscillator is usually variable so that it is possible to compensate for frequency drift or to obtain a baseband signal. This type of digitizer requires the provision of two channels which are as closely identical as possible, with regard to the filter characteristics, the gain, and the characteristics of the sampler and the analog-digital converter. This balance between the two channels is difficult to achieve and calls for a large number of components.
To avoid this problem of balancing two channels, other types of analytical digitizer determine the values of the two components in phase quadrature using a single sampler and a single analog-digital converter followed by two digital channels which perform different processing. There is no longer any balancing problem as the two components can be determined from the same sequence of sample values. The article "Digital Processing for Positioning With One Satellite" by A. Marguinaud, published by Advisory Group for Aerospace Research and Development, 7 rue Ancelle 92200 Neuilly sur Seine, France, describes an analytical digitizer in which the two digital channels comprise two finite impulse responses filters. This digitizer uses a method based on uniform representation of any continuous signal by a sum of trigonometrical functions, in accordance with the Weierstrass theorem: The real component x(t) and the quadrature component y(t) of any continuous real signal can be represented as follows: ##EQU1## where n depends only on the tolerable error between the real signal and its approximation.
In the case of limited bandwidth signals, sampling theory allows the angular frequencies j.omega. to be replaced by their value modulo ##EQU2## where .DELTA.t is the sampling time increment. As a result, the only components to be taken into account in the theoretical considerations are in the physical band. In practise, this applies whenever the sampler is preceded by a bandpass filter.
This article teaches that an analytical digitizer is particularly simple to implement if the filters process only four samples and the center frequency of the signal to be processed is equal to one quarter of the sampling frequency. It gives values of the coefficients a.sub.0, a.sub.1, b.sub.0, b.sub.1. The two filters then calculate the two components from the following equations: ##EQU3## where a.sub.0 =3
b.sub.0 =3 PA1 a.sub.1 =-1 PA1 b.sub.1 =1
This article also teaches that the noise due to digitization of the signal and to the calculations carried out by the filters, referred to as quadrature noise, is such that the signal/noise ratio is 20 dB if the bandwidth is equal to one quarter of the signal center frequency or 30 dB if the signal bandwidth is equal to half the signal center frequency.
The article "Traitement Analytique du Signal" by A. Marguinaud, published by the French Ministry of Defense (Ministere de la Defense; Direction Generale de l'Armement Direction des Recherches, Etudes et Techniques; 4 rue de la Porte d'Issy, 75015 Paris); teaches that the weighting coefficients must be limited to symmetrical coefficients a.sub.0, . . . , a.sub.h, a.sub.h, . . . , a.sub.0 for a first component of the signal and anti-symmetrical coefficients b.sub.0, . . . , b.sub.h, -b.sub.h, . . . , -b.sub.0 for the second component.
This article also suggests determination of the coefficients which are matched to the spectrum of the signal to be processed.
A heuristic method which carries out a simulation on a computer determines weighting coefficients for four or even six samples but a heuristic method does not yield coefficient values of sufficient accuracy if the number of samples is greater than six.
An object of the invention is to propose a method of calculating coefficients for an analytical digitizer including two finite impulse response filters for processing more than four samples, weighting them by coefficients determined by a rigorous general method so that it is possible to optimize the quadrature signal/noise ratio and the complexity of the implementation of the digitizer for each application, i.e. according to the spectrum of the received signal and the quadrature signal/noise ratio required for that application.
Another object of the invention is to propose an analytical digitizer in which the number and the value of the weighting coefficients vary automatically according to the characteristics of the signal received for applications such as radio surveillance receivers in which the characteristics of the signal received are not constant.